Aligning rectilinear images in 3D through projective registration and calibration

ABSTRACT

An improved apparatus and method for creating high quality virtual reality panoramas is disclosed that yields dramatic improvements during the authoring and projecting cycles, with speeds up to several orders of magnitude faster than prior systems. In a preferred embodiment, a series of rectilinear images taken from a plurality of rows are pairwise registered with one another, and locally optimized using a pairwise objective function (local error function) that minimizes certain parameters in a projective transformation, using an improved iterative procedure. The local error function values for the pairwise registrations are then saved and used to construct a quadratic surface to approximate a global optimization function (global error function). The chain rule is used to avoid the direct evaluation of the global objective function, saving computation. In one embodiment concerning the blending aspect of the present invention, an improved procedure is described that relies on Laplacian and Gaussian pyramids, using a blend mask whose boundaries are determined by the grassfire transform. An improved iterative procedure is disclosed for the blending that also determines at what level of the pyramid to perform blending, and results in low frequency image components being blended over a wider region and high frequency components being blended over a narrower region. Human interaction and input is also provided to allow manual projective registration, initial calibration and feedback in the selection of photos and convergence of the system.

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation of U.S. patent applicationSer. No. 10/077,102 for “Aligning Rectilinear Images in 3D ThroughProjective Registration and Calibration,” filed Feb. 14, 2002, which isa continuation of U.S. patent application Ser. No. 09/160,822 for“Aligning Rectilinear Images in 3D Through Projective Registration andCalibration,” filed Sep. 25, 1998, now U.S. Pat. No. 6,434,265, thedisclosures of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of Invention

[0003] The present invention relates generally to an improved system forcreating a full 360-degree virtual reality panorama from rectilinearimages.

[0004] A panorama is a compact representation of the environment viewedfrom a 3D position. While an ordinary image can capture only a smallportion of the environment, a panorama can capture it all, or anyportion of it, depending on the geometry in which the panoramas arerepresented. Recently there has been an explosive popularity ofpanoramas on the world wide web and in multimedia as an effective toolto present a photo-realistic virtual reality. However, creatinghigh-quality panoramas, especially those that completely enclose space,has been difficult.

[0005] 2. Description of Related Art

[0006] Various systems have been proposed for simulating a virtualreality environment using photographic quality images. Many virtualreality environments use 3D models or mathematical equations to create asimulated world. The user explores this simulation in real time. Though3D modeling via equations has certain advantages, such as a depiction ofa scene from any arbitrary vantage point, creating images from equationsgenerated by a computer is seriously limited by the speed of thecomputer. To avoid this problem, technology such as QuickTime™ VR fromApple Corporation uses images that have already been produced, eitherphotographically or generated by a 3D modeling program, and stored insecondary memory. Software only has to read the image files from a diskand display the scene as needed, rather than calculating the scene frommathematical models. However, a limitation of the QuickTime™ VR programis that it requires that the view direction for photos reside in asingle plane, such as that obtained by rotating a camera on a tripod. Italso requires that the vertical field of view (or equivalently, thefocal length) be known, and that there be roughly equal angularincrements between one photo and the next.

[0007] Further, a panoramic movie or image can be created usingspecialized hardware, such as with a panoramic camera or a fisheye lenscamera. However, such hardware is inconvenient for the average novicephotographer. In the altemative, software can be used to simulate apanorama. This obviates the need for specialized hardware.

[0008] Though various software programs have been proposed to simulatepanoramas without the use of special hardware, these programs havecertain serious drawbacks that have not been successfully overcome todate. These include, but are not limited to, unrealistic representationsof images, lack of proper registration and calibration of images, lackof proper blending of images, and slow speed in registering, calibratingand blending images to create a panorama.

SUMMARY OF THE INVENTION

[0009] Accordingly, one aspect of the present invention is to provide animproved system and method for overcoming the drawbacks of priortechniques discussed above.

[0010] Another aspect of the present invention is to provide for theregistration, calibration and global optimization of images, preferablycaptured from a substantially single nodal position. The solution tocreating a full 360-degree panorama quickly and seamlessly is dividedinto three steps. The first step registers all overlapping imagesprojectively. A combination of a gradient-based optimization method anda correlation-based linear search has proved to be robust in cases ofdrastic exposure differences and small amount of parallax. The secondstep takes the projective matrices and their associated Hessian matricesas inputs, and calibrates the internal and external parameters of everyimage through a global optimization. The objective is to minimize theoverall image discrepancies in all overlap regions while convertingprojective matrices into camera parameters such as focal length, aspectratio, image center, 3D orientation and the like. Improved techniquesfor global optimization are disclosed that give order of magnitudeimprovements over prior systems of optimization. The third stepre-projects all images onto a panorama by a method employingLaplacian-pyramid based blending using a Gaussian blend mask generatedby the grassfire transform. The purpose of the blending is to provide asmooth transition between images and eliminate small residues ofmisalignments resulting from parallax or imperfect pairwiseregistrations. The invention further provides for human interaction,where necessary, for initialization, feedback and manual options.

[0011] Further, the present invention, unlike some of the prior art,allows for multiple views, from multiple planes and rows of images, andallows for the arbitrary orientation of photographic images to beconstructed into a panorama, without specialized hardware such as atripod or fisheye lens. In addition, the present system and method canbe several orders of magnitude faster than the prior art.

[0012] The numerous aspects of the invention described herein result ina system for registration, calibration and blending that creates highquality panoramas from rectilinear images that is up to several ordersof magnitude faster than prior systems. In one calculation, the presentinvention is up to 100,000 times faster than prior techniques. As aconsequence, the present invention could be used to construct panoramasmuch quicker than previous methods. These panoramas can be used inapplications where real-time image rendering is important, such as inreal-time 3D virtual reality, the construction of background images,computer animation, multimedia, and the like.

[0013] The above described and many other features and attendantadvantages of the present invention will become apparent from aconsideration of the following detailed description when considered inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Detailed description of preferred embodiments of the inventionwill be made with reference to the accompanying drawings.

[0015] FIGS. 1 (a) and 1 (b) is an artists rendition of a compositephotograph before and after the application of the present invention.

[0016]FIG. 2 is a generalized flowchart of the various function modulescomprising one embodiment of the present invention.

[0017]FIG. 3 is a generalized flowchart of the method of operation ofthe Pairwise Registration function module of one embodiment of thepresent invention.

[0018]FIG. 4 is a generalized flowchart for the method of operation ofthe Calibration and Global Optimization function module of oneembodiment of the present invention.

[0019]FIG. 5 is a generalized flowchart for the method of operation ofthe blending function module of one embodiment of the present invention.

[0020]FIG. 6 is a screen shot of a user interface dialog window for theuser interface of one embodiment of the present invention.

[0021]FIG. 7 is a conceptual illustration on the problem of finding theproper Laplacian pyramid level using the minor axis of an inertialellipse.

[0022]FIG. 8 is a graphical illustration of the transition lengths fordifferent frequency image components (low, middle and high) used in oneembodiment of the blending function module of the present invention.

[0023]FIG. 9 conceptually illustrates the weighted average method forblending.

[0024] FIGS. 10 (a) and (b) illustrate the blend mask used for blendingtwo images during the blending phase of one embodiment of the presentinvention.

[0025] FIGS. 11 (a) and (b) illustrate a particular problem overcomeduring blending in one embodiment of the present invention.

[0026]FIG. 12 illustrates a particular virtual reality orientation ofimages for the user interface for one embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0027] Disclosed herein is a detailed description of the best presentlyknown mode of carrying out the invention. This description is not to betaken in a limiting sense, but is made merely for the purpose ofillustrating the general principles of the invention. The section titlesand overall organization of the present detailed description are for thepurpose of convenience only and are not intended to limit the presentinvention.

[0028] Turning to FIG. 1, there is shown a simulation of differentoverlapping rectilinear images, or 2D photographs, framed by dashedlines during the authoring portion of the present invention, asindicated by dashed lines 110. Where the images overlap there ispotential for misalignment when constructing a 3D panorarma, asindicated by blurry lines 112, for a variety of reasons, including thearbitrary position of the camera, errors in internal and external camerapararmeters, and, distortions that occur when warping a 2D image toconstruct a 3D image space. The present invention is designed tocalibrate and align all such 2D rectilinear images with respect to oneanother and globally, blend the images where they overlap, and constructa reconstructed and relatively error free 3D panorama image, shownconceptually in 2D form as FIG. 1(b), for any arbitrary geometry.

[0029]FIG. 2 discloses a generalized flowchart for overall operation ofthe invention. The invention is part of a system 210 comprising acomputer, having all necessary hardware, such as processing unit 212,e.g., a G3 microprocessor chip; I/O 214, such as a keyboard 216, videomonitor 218, and mouse 217; memory 220, which may be any sort of memorybuffer, preferably primary memory, e.g. RAM, that can be cached tosecondary memory, such as a hard drive. The system 210 is controlled bya program residing in system memory 220, which also stores output dataand other data. The program is preferably written in the C or C++language, using classes, structures, functions, calls, translationunits, headers, subroutines, modules, and other features of structuredprogramming, where appropriate, of both data and source code, suitablycompiled and in executable form, in accordance with the teachings of thepresent disclosure to practice the invention. The present invention isalso suitable for implementation with an interpreted language such asJava.

[0030] In constructing a panorama from rectilinear images, the systemfinds solutions to three sub-problems: (1) the projective registrationsof overlapping images (shown as the “local pairwise registration” box222 in FIG. 2), (2) calibration and global optimization of these images,a self-calibration in which 2D image planes are positioned as 3D planesin space (shown as the “calibration and global optimization” box 224 inFIG. 2), and (3) the composing or blending problem in which images areready to be reprojected to a 3D environment map with pixels in overlapregions being composed from multiple images, to smooth any transitionaldiscontinuities (shown as the “blending” box 226 in FIG. 2). Finally,there is the projection or construction of the assembled panorama onto a3D geometry surface, such as a cylinder, cube or sphere (defined as the“projection” box 228 in FIG. 2).

[0031] The solutions to these sub-problems are performed by softwarefunction modules 222, 224, 226, 228 residing in memory 220 and operatingthe processor 212. The modules are designated, as explained furtherherein, the pairwise registration function module 222, the calibrationand global optimization function module 224, the blending functionmodule 226, and the projection function module 228. A user interfacemodule 230, also residing in memory 220, may interact with the othermodules to pass data to and from the modules, and accept input from ahuman user of the system. The modules may receive data from memory,manipulate that data as described herein, and output the data to othermodules. The three modules 222, 224 and 226 may perform feedback to passdata back to previous modules, as indicated by arrows 233, and asdescribed below. Although in a preferred embodiment the modules areprogrammed as separate software routines or classes, the modules may becombined into one module performing all the designated tasks performedby separate modules.

[0032] As a final step, the fourth module, the projection functionmodule 228, constructs a panoramic scene by projecting the blended imageonto any designated geometry view surface, typically a cubic,polyhedral, cylindrical or spherical surface. The projection module maybe controlled through the user interface 230 as well, to allow a user toselect what geometry will be projected onto and to control and modifyother factors, including the use of photo re-touching software such asPhotoShop™ for modifying the final panorama.

[0033] Generally, the local registration, self-calibration and globaloptimization, and blending involve a multi-step procedure.

[0034] First, regarding the initial local registration, and referringgenerally to the generalized flowchart of FIG. 3, the system 210 readsin each overlapping rectilinear image into main memory 220, as indicatedby step 312. The images are assumed to roughly share a common nodalpoint (i.e., that point in the three-space where all rays of lightconverge through a lens) with other overlapping rectilinear images. Theobject of the program during local registration is to register thelocally overlapping images, by comparing common overlapping areasbetween overlapping images at certain predetermined resolution levels ona Gaussian pyramid representing the overlapped images. Differentcombinations of overlapping areas are tried to achieve the optimaloverlap between images (or, equivalently, the smallest error in theerror function or pairwise objective function described herein) usingthe steps described herein, which generally minimizes the averagesquared pixel intensity (e.g., brightness and contrast) difference withrespect to certain transformation parameters. Initial values forparameters used in optimizing the pairwise objective function areassumed by the computer, as indicated in step 314. The initial valuesmay optionally be input by a user, e.g., with a user interface 230 as inFIG. 2, and in response to a user dialog window such as of the kindshown in FIG. 6. Besides the global orientation (pan, tilt and roll) theother parameters that are most likely to give instability in convergenceof the error function are bad initial estimates of the brightness andcontrast, as well as of the geometric image center of projection of theoverlapping rectilinear images. Certain parameters most likely to createinstability in the convergence of the local error functions can becontrolled (e.g., progressively dampened at different levels of theGaussian pyramid) to ensure convergence, as indicated by step 318. Theoverlapping images are then perturbed and the local error function withrespect to these and other variables is calculated until a minimal localerror function is found, as indicated by step 320. The minimal localerror function is then stored for a particular level of the Gaussianpyramid, as indicated in step 322, for each pairwise registration, andis saved and later used to compute a global error function for all theoverlapping images. The local pairwise registration module 222 iteratesuntil the entire Gaussian pyramid is traversed, starting from thecoarsest level of the pyramid (sometimes called the bottom, where thepyramid can be standing on its inverted top) and working to the finestlevel resolution, as indicated in decision box 324. It should be notedthat at any stage throughout the registration, and throughout theinvention in general, the system may check for a user interruption,through the user interface, that would require immediate attention fromthe processor, such as to allow the user to interactively adjust theparameters to avoid divergence or convergence to an undesired localminimum.

[0035] As indicated in box 316 of FIG. 3, it must be determined at whatlevel in the Gaussian pyramid to start the local pairwise registration.One way to find the lowest level is to select the resolution level atwhich it is found that the images share at least some arbitrary numberof overlapping pixels, e.g., preferably about 30 pixels from each side,e.g., preferably no less than 30 pixels across the overlapping area. Ifgreater than 60 pixels of overlap is found in these areas, the size(resolution) of the overlap region is decreased by half (going deeperinto the pyramid) and the procedure of the present invention isreiterated again. If, on the other hand, the overlap is less than 30pixels, then the size (resolution) of the overlap region is increased bydoubling. By utilizing multi-resolution. registration of overlappingimages by way of the Gaussian pyramid, convergence to the desiredoptimum is accelerated, and false local minima are avoided.

[0036] On occasion, it may be visually apparent to a user that duringregistration the images are not converging optimally. In this case userinput may manually abort the pairwise registration procedure, and theuser may manually help align the images closer before resuming automaticregistration, as before. This manual intervention is true for allaspects of the invention. Nevertheless, the present invention issurprisingly robust, and manual intervention is not a prerequisite forthe invention to work.

[0037] Non-optimal convergence or divergence has sometimes been found tobe the case whenever images for a spherical projection are used,especially those in the “pole” regions of the sphere (though in generalthe invention can adjust quite nicely for images that wrap around thepoles). Divergence sometimes results when the initial default parameterschosen are wildly off or not suitable for convergence. During suchinstability, the images will appear to a user to “run away” from eachother. In this case, and throughout the invention, provision may beprovided in the user interface 230 of the embodiment of FIG. 2 of thepresent invention for manual intervention, such as to abort the program,for the manual selection and relative positioning of the images to bepairwise registered, and for the selection and relative positioning ofoverlapping images for blending.

[0038] The iterative method of moving down a pyramid when an overlapregion is greater than, say, 30 pixels, is an attempt to preventinstability in the error function due to problematic parameters, such asinitial value errors in the image center of projection of the imagesbeing registered, and errors in setting initial brightness and contrastvalues. Techniques of damping and annealing of problematic parameters(with damping progressively diminished and finally set to zero as onemoves up the pyramid to finer levels) can be used to stabilize the localerror function for these problematic terms, as explained further herein.

[0039] One improvement over prior techniques has been to save the localerror function values and use them to compute and optimize the globalerror function needed for optimization. This improvement also avoidshaving to evaluate the entire global error function (global objectivefunction) from scratch. The pairwise objective functions (local errorfunctions) are approximated by a quadratic Taylor series, and, togetherwith the chain rule, the global objective function (global errorfunction) is minimized. Calculation of the global error function isgreatly speeded up by this procedure.

[0040] Further regarding rectilinear images taken in a non-arbitrarymanner (such as from a tripod that is rotated, or a photographer whomanually “pans” a field of view), the number of pyramid levels andoptimal direction for the blending of images overlapping in a region canbe computed by the present invention by computing the minimum eigenvalueof the 2×2 inertial tensor of the overlapping region between two images.It has been found in practice that for an arbitrary polygon representingan overlapping region, the optimal direction for blending, as well asthe width of the blending region (which determines the level in thepyramid at which to start the method of registration and optimization)is found along the minor axis of the inertial ellipse found from solvingfor the inertial tensor of the overlapping images. A similar method offinding the proper pyramid level is by solving for the smallesteigenvalue of an inertial tensor of the overlap region between images.Conceptually, such an ellipse is shown in FIG. 7. The blending region inan arbitrarily shaped polygon region 710, which represents the area ofoverlap between overlapping images, lies along the width and directionof the minor axis 712 of the ellipse 714, which is-calculated from theinertial tensor of the overlapping images forming the polygon.

[0041] Thus, the results from computing the inertial tensor are used todetermine the pyramid level, blending width, and blending direction. Thesmallest inertial eigenvalue is used to determine the number of pyramidlevels. One could also use the eigenvalue vector (eigenvector) todetermine the direction, or, preferably, use a blending mask, asexplained herein, that yields a grayscale ramp, which defines directionin a direction field from taking the grayscale ramp gradient.

[0042] Next, after pairwise local registration, global optimization isused to remove any inconsistencies. The parameters found at the localregistration level, generally from six to ten parameters per overlappingimage pair, are optimized globally. Various constraints ensureoptimization whenever there are suitable overlapping image pairs, as thenumber of independent parameters is usually less than the constraints.Regarding optimization in general, to ensure the best chance forconvergence of a solution a combination of simulated annealing andprogressive damping is used, as described herein.

[0043] Global optimization is necessary because noise in the images willyield inconsistencies in cyclically overlapping sets of images (e.g.,that A is pairwise registered with B, B with C, and C with A, does notnecessarily mean A and C are properly globally registered with C and B).During the global optimization phase, the discrepancies are distributedamong all image pairs in such a way as to minimize the increase in totalerror. The Hessian matrix, computed in the local registration phase, asdescribed further herein, provides a description of the shape of theerror function landscape in the neighborhood of each pairwise optimum.Parametric perturbations occur along the valleys of this landscape (asindicated by the Hessian), where the increase in error is minimal. Oneway of looking at this solution is to say that knowledge gathered fromthe pairwise registration optimization is saved and used for globaloptimization, avoiding additional computation.

[0044] Turning attention to FIG. 4, there is shown a generalizedflowchart for the calibration and global optimization module of thepresent invention. Data from the local pairwise registration module 222is provided to the calibration and global optimization module 224, asindicated by box step 402. Such data can include the pairwise objectivefunctions (local error function values) for each pairwise registrationfound previously. The global objective function is calculated from suchdata, as indicated by boxes 404, 406, and as described more fully below.The alignment of images globally is checked to ensure globalregistration, as in decision boxes 410 and 412, which may accept manualinput from a user, via a user interface module. If there is alignment,the system proceeds from the calibration and global optimizationfunction module to the blending of images. Otherwise, as illustrated byboxes 418 and 420, the pairwise registration module parameters (such asshown by box 314 in FIG. 3) may be re-initialized and the pairwiseregistration module reexecuted to recompute the pairwise registration ofimages, using better, updated camera parameters as determined from theglobal registration procedure as shown in FIG. 4.

[0045] During the blending step of the procedure utilized by the systemof the present invention, the image overlap regions are “blended” or theimages are “stitched” together, so that the high frequencies (e.g.,sharp lines of contrast, such as edge boundaries, analogous to the highfrequency signals associated with a square wave) are blended over anarrow blend region range, and the low frequencies (e.g., illuminationvariations, analogous to DC baseband signals) are blended over a widerange. In this way the images are seamlessly integrated to form apanorama in an aesthetic manner.

[0046] In one preferred embodiment of the invention, as illustrated bythe steps in FIG. 5, blending is performed by determining the coarsestlevel in a Laplacian pyramid for which to begin blending of images I, J(box 504), and constructing a Laplacian pyramid at this level (box 506).One of the two images may be comprised of previously blended images. Ablend mask boundary is generated (box 508), defining the boundary overwhich blending is to occur, preferably using the “grassfire” transformmethod. Next, a blend mask is generated by a Gaussian pyramid method(box 508). In one preferred embodiment, the overlapping images I and Jthat are to be blended are put into a Laplacian pyramid and multipliedby the blending mask, or its compliment, respectively (box 510). Theresulting product is repeatedly added together to each level of theLaplacian pyramid (box 512), moving up to the finest level resolution ofthe pyramid in a sequential fashion (decision box 514), until a blendedimage is achieved for the two images. A similar procedure is performedfor all other images that overlap, as indicated by decision box 516.This preferred technique has the advantage over prior techniques in thatlow frequency component images are blended over a wider area region,giving a smoothing effect, as desired for low frequency components,while high frequency components (such as sharp edges) are blended over asmaller blend region, giving a “sharpening” effect for these highfrequency components, exactly as desired. This is illustratedconceptually by FIG. 8.

[0047] Authoring a panorama from 2D images can be thought of as dividedinto two different phases: (1) orientation of originally 2D images into3D space, and (2) the projection of a panorama onto a particular 3Dgeometry, that can later be used to project views of the panorama onto a2D viewing plane. A series of preferably overlapping photographs areanalyzed to determine what orientation the photographs were taken inorder to establish a common ground for subsequent operations, includingthe construction of a panorama. The panorama is not ordinarily meant tobe viewed by a user, only the subsequent projection of the panorama ontoa viewing plane is viewed by the user. The panorama is constructed on aparticular geometry that will best facilitate the subsequent step(sometimes termed rendering) of the projection of the panorama from theparticular geometry onto a chosen viewing plane for viewing by a user.Typical geometries in the system of the present invention on whichpanaoramas are formed include: cubic, polyhedral, cylindrical andspherical geometries. However, any type of geometry may be used, such astwo frusto-conical cones joined at their base with the apexes pointingaway from one another; any quadric surface, and any and all of thegeometries that employ the following projections: equidistant,equiangular, ellipsoid, Mercator (and all derivatives thereof, e.g.,transverse Mercator, Oblique Mercator, and the like), cylindricalequal-area, Miller cylindrical, equidistant cylindrical, Cassini (e.g.,both for spherical and ellipsoid projections, and the like), all conicmap projections, e.g., Albers equal-area, Lambert conformal conic,equidistant conic, bipolar oblique conic conformal, polyconic, Bonne,all azimuthal and related projections, e.g., orthographic, sterographic,gnomonic, general perspective, Lambert azimuthal equal-area, azimuthalequidistant, modified-stereographic conformal, all space mapprojections, including space oblique Mercator and satellite-trackingprojections, all pseudocylindrical and other miscellaneous projections,including Van der Grinten, sinusoidal, Mollweide and Eckert IV and VIprojections. The foregoing list is meant to be illustrative and notexhaustive of the geometries and projections possible during theconstruction and employment of panoramas using the system of the presentinvention.

[0048] Further, the present invention can be employed in future systemsthat are fast enough to eliminate the need for a projection functionmodule 228, and proceed directly from pairwise registration, calibrationand global optimization to the viewing and blending of the panorama on achosen viewing plane, without loss of generality. Presently, however,there is not sufficient computing power in most desktop computers forthis to be feasible for real time applications.

[0049] Furthermore, the system of the present invention has means for auser interface for all phases of the invention. A user may select, amongother things, which images are to be registered, and at what arbitraryimage plane. The user interface, suitable for display on a computermonitor and with input from a keyboard, mouse pointer, or other I/Odevice, has fields for any and all internal and external parameters ofthe projection matrix of the images, including aspect ratio, number ofrows of images, the tilt between rows, the angle between photos within arow, the roll of each image taken (e.g., landscape mode), as well asfields for how many horizontal rows of images are to be registered(typically two or more), image center position, focal length of camera,camera orientation with respect to a common reference frame, such ascamera pan, tilt, roll and skew, and the brightness and contrast ofimages. The user interface may have the ability to adjust theaforementioned parameters for each image individually, or may have theability to adjust parameters for images captured with a particularmethodology, such as equal angular increments in latitude and longitude.

[0050] Thus, turning attention now to FIG. 6, there is shown a screenshot of a user interface for the present system, suitable forinitialization parameters for an ensemble of images, captured with anequal angular increment methodology that can be facilitated by use of atripod. The user interface is particularly useful for authoringpanoramas when a user wishes to adjust the automatic default orientationgenerated by the computer for the present invention. A more complex userinterface may be provided to accommodate the initial orientation andplacement of a free-form set of images, i.e. a set of images capturedwithout any particular methodology, such as that captured using ahand-held camera. A plurality of parameters of the kind described hereinmay be manually entered into the dialog box fields by the user (ifknown) to aid in the pairwise registration, calibration and globaloptimization and blending of images. Further, the particular imagesselected for pairwise registration and calibration and globaloptimization may be aborted during non-convergence run-away conditions.Some of the parameters that may be explicitly specified by a userinclude (referring to FIG. 6) the number of rows 602 (assuming a panningof photos are taken, with a number of overlapping rows of photos takenabout a 360 degree arc), initial pan 604, initial tilt 606, panincrement 608 and initial roll 610 for the first row of photos (rows arepreferably used, but vertical columns of photos are also contemplated);and, for inter-row parameters; the pan increment 612, roll increment 614and tilt increment 616. Zoom lens distortion factors and othermiscellaneous factors may be entered in dialog fields such as field 620.Other parameters may be specified for overriding the computer defaultsand for better guaranteeing convergence, such as camera focal length orf-stop, pixel aspect ratio, and the like. In addition, the userinterface may allow for the selection, arrangement and relativepositioning of photos to be composed into a panorama, preferably in arow by row layout, with preferably at least one or more rows of photosto be made into the panorama.

[0051] Further, while one preferred embodiment of the present system isdesigned for overlapping image pairs to share a common nodal position,in general the system is forgiving of nodal point changes, provided thechanges are not excessive, e.g., a 1% shift in nodal point should stillallow satisfactory panoramas to be formed. The one-percent shift is notoverly cumbersome when taking long range photos, e.g., from the heightof the 300 m Eiffel Tower a 1% shift will allow up to 3 meters (nearly10 ft) of shifting of camera nodal position when taking photos at thebase, which can accommodate an amateur photographer taking pictureswithout a tripod.

[0052] Turning attention again to the three modules labeled PairwiseRegistration, Calibration and Global Optimization and Blending, asillustrated in FIG. 2, the authoring aspect of the invention will befurther described.

[0053] I. Pairwise Registration

[0054] To find a solution to the first sub-problem posed in constructinga panorama from rectilinear images, finding the projective registrationsof overlapping images, one must pairwise register the two images.Pairwise registration can be thought of as synonymous to finding anestimate of the projective transformation relating two given overlappingrectilinear images. The projective transformation may be represented bya particular parametrized projective matrix, that is parametrized by atypical canonical number (usually 8 or 9) projective parameters, e.g.,3D rotation parameters (pan, tilt roll), center of projection of images,ratio of focal lengths, and the like. The projective matrix can bedefined as a particular case of a three-dimensional affinetransformation, a transformation that effects rotation, scaling, shearand translation, with the restriction that camera motions arerotational. As is known per se, transformations are important tools ingenerating three-dimensional scenes, in moving objects around in anenvironment, and in constructing a two-dimensional view of theenvironment.

[0055] The mathematics described herein are but one representation forthe method carried out by the apparatus of the present system for one ormore preferred embodiments of the invention. In mathematics the samephenomena can be represented in different symbolic notation—which oftenappear to the untrained eye as being radically different from oneanother—without changing the nature of the phenomena described. Forexample, as explained above and represented further below, theprojective transformation of a pair of images can be more particularlycharacterized as a projective transformation that is particularized as aprojective matrix parametrized by a certain projective matrix parameters(typically having 8 or 9 projective parameters, as explained herein,such as pan, tilt, roll, center of projection of the images, ratio offocal lengths, and the like). However, this particular representationdoes not preclude the projective transformation from being reduced topractice using the teachings of the present invention by alternateequivalent methods or other representations, other than as representedby a particular parametric matrix representation, without loss ofgenerality from the way the invention is described herein. Further, andconcomitantly, the transformations involved with the present inventionmay be described in alternate notation, using for example Euler anglesor quatemions, without detracting from the spirit and scope of theinvention. It is to be understood from the teachings of the presentdisclosure that the description of a projective matrix also includesthese other representations. By the same token, programming constructssuch as data structures and classes are typically realized in binarycode, rather than abstract mathematical notations, and, as such,constitute the machine readable representations of the constructs. Therepresentation of such constructs in this form do not result in any lossof generality of the representation of the underlying invention asdescribed herein.

[0056] Regarding local pairwise registration in general, if onerestricts camera motions to be rotational only, the 2D warping betweenimages i, j, is strictly projective in absence of lens distortions, andgiven by, [Eq.(1)] $\begin{matrix}{\begin{bmatrix}x_{i} \\y_{i} \\z_{i}\end{bmatrix} = {\begin{bmatrix}m_{0} & m_{1} & m_{2} \\m_{3} & m_{4} & m_{5} \\m_{6} & m_{7} & m_{8}\end{bmatrix}\begin{bmatrix}x_{j} \\y_{j} \\z_{j}\end{bmatrix}}} & (1)\end{matrix}$

[0057] where:[_(x) _(i) _(y) _(i) _(z) _(i) ]^(T) are the homogeneouscoordinates of pixel locations (with the convention that column vectorsrepresent three-dimensional points). In the following description, thevector X_(i) represents the homogeneous coordinates, and the matrixM_(ij) represents the matrix that transforms coordinates from image j toimage i. Due to the scale ambiguity in the projective matrix, the lastparameter m₈ in the projective matrices is set to equal 1.

[0058] The objective of local pairwise registration is to estimate theprojective matrix given two overlapping images. The projective matrix isinitialized by the camera internal and external parameters, e.g.,[Eq.(2)]

M _(ij) =T ⁻¹(p _(i) ,q _(i))T(p _(j) ,q _(j))  (2)

[0059] [Eq.(3)]

[0060] where $\begin{matrix}{{T\left( {p_{i},\quad q_{i}} \right)} = {{R\left( q_{i} \right)} = {{R\left( q_{i} \right)}\begin{bmatrix}1 & 0 & {- C_{x}^{i}} \\0 & a_{i} & {- C_{y}^{i}} \\0 & 0 & f_{i}\end{bmatrix}}}} & (3)\end{matrix}$

[0061] where [C^(i) _(x), C^(i) _(y], a) _(i), f_(i) are the imagecenter position, the aspect ratio and the focal length, respectively;

p_(i)=[a_(i), f_(i), C^(i) _(x), C^(i) _(y)]^(T)

[0062] is the internal parameters vector;

[0063] q_(i)=represents the camera orientation with respect to a commonreference frame; and

[0064] R( )=represents the 3×3 rotation matrix computed from theorientation parameters q_(i).

[0065] Camera internal and external parameters are initialized eitherautomatically by the computer assuming default values, or manually withuser input.

[0066] There are ten parameters in the projective registration: eightindependent parameters in the projective matrix and two parameters tocompensate for brightness and contrast difference between the twoimages. The gradient-based optimization minimizes the followingobjective, as suggested in box 320 in FIG. 3, by instructing theprocessor 212 to perturb the overlapping images stored in memory withvarious combinations of overlapping pixels until the below localregistration error function has the smallest value [Eq. 4]:$\begin{matrix}{e_{ij} = {\frac{1}{A_{ij}}{\sum\limits_{\quad {overlap}\quad}^{\quad}\quad \left( {{s_{ij}{I_{j}\left( X_{j} \right)}} + b_{ij} - {I_{i}\left( {M_{ij}X_{j}} \right)}} \right)^{2}}}} & (4)\end{matrix}$

[0067] where s_(ij) and b_(ij), the exposure parameters, represent theexposure difference, I_(j)( ) and I_(j)( ) are pixel intensity valuesfrom the two images, and A_(ij) is the overlap area (which helpsnormalize the error function e_(ij)). The optimizations are performed onprogressively finer levels of Gaussian pyramids. In practice, however,it has been found that the direct application of gradient-basedoptimization frequently failed due to exposure differences, largetranslations, or both. Therefore, preferably a combination ofcorrelation-based linear search and a progressive damping (e.g.,simulated annealing) of exposure parameters is used to alleviate theproblem, as suggested by box 318 of FIG. 3. On the coarsest pyramidlevel (e.g., ‘lowest’ resolution level of the image, the method of theinvention first performs a linear search over the transitionalparameters using normalized correlations, an idea similar to aprogressive complexity search known per se in the art, e.g., see H.Sawhney and R. Kumar, “True multi-image alignment and its application tomosaicing and lens distortion correction”, Proc. of CVPR, pp. 450-56(1997). Since the image size on the coarsest pyramid level is small, thecorrelations are done efficiently. Once the maximal correlations arefound, the exposure parameters s_(ij) and b_(ij) are estimated through alinear regression. When the gradient-based optimization is performed onsubsequent finer pyramid levels, the damping coefficients on exposureparameters are reduced exponentially, and finally set to zero at thefinest pyramid level.

[0068] To determine the number of pyramid levels given an arbitraryoverlap of two images, one can compute the eigenvalues of the 2×2inertial tensor of the overlap polygon region. Determining eigenvaluesand inertial tensors are known in the art per se. The square root “I” ofthe smaller eigenvalue is used to estimate the number of pyramid levelsaccording to the formula: $\begin{matrix}{\log_{2}\left( \frac{l}{l_{\min}} \right)} & (5)\end{matrix}$

[0069] where I_(min) is the minimal size of the finest level resolutionpyramid level. In a preferred embodiment, I_(min) is set to 10 pixels.

[0070] II. Calibration and Global Optimization

[0071] The second major step in authoring panoramas is to extract camerainternal and external parameters from those projective matricesestimated in step 1. above. In general, it is impossible to achieve adirect solution by inverting Eq. (2) above directly to obtain the cameraparameters, since there are eleven camera parameters while a projectivematrix provides only eight constraints. However, because one imageusually overlaps with multiple images, one can take advantage ofredundancy in the system to obtain a consistent set of camera parametersthat approximates all projective matrices in the same time. A globaloptimization routine module is used to achieve this goal.

[0072] Since the projective matrix is a function of camera parameters asin Eq. (2), to extract all camera internal and- external parameters thefollowing objective functions are minimized by having the calibrationand global optimization module 224 of FIG. 2 instruct the processor toperturb different combinations of images stored in memory to minimizethe following global error function: [Eq. (6)]

E=Σ _(ij) A _(ij) e _(ij)(M _(ij)(p _(i) ,q _(i) ,p _(j) ,q _(j)))  (6)

[0073] where e_(ij) is the pairwise objective function in Eq. (4).

[0074] However, it has been found that it is computationallyprohibitively expensive to evaluate the objective functions according toEq. (6). By noting that the pairwise objective function e_(ij) hasalready been optimized individually, we can approximate it by aquadratic surface, which can be viewed as terms from a matrix TaylorSeries expansion. Thus, in a preferred embodiment, the followingapproximation is used in the calibration and global optimization routinemodule: [Eq. (7)]

e _(ij)(M _(ij))≈e ⁰ _(ij)+(M _(ij) −M ₀ _(ij))^(T) C _(ij)(M _(ij) −M ⁰_(ij))  (7)

[0075] where e_(ij) ⁰ is a constant representing the minimal valueachieved in the pairwise registration; M_(ij) ⁰ is the 8×1 vectorrepresenting the optimal projective matrix, and

[0076] C_(ij) is the 8×8 Hessian matrix obtained when optimizingobjective function e_(ij), as in the methods of Levenberg-Marquardt orBroyden-Fletcher-Goldfarb-Shanno, known in the art per se. Thus theprojective matrix can be treated as an 8×1 vector instead of a 3×3matrix. This step is represented in FIG. 4 as box 404 Other methods maybe employed in the present invention using the teachings herein withoutdeparting from the scope of the invention.

[0077] Next, once the pairwise objective functions are approximated byquadratic surfaces with Eq. (7), the global objective function in Eq.(6) is used as a weighted sum of all those quadratic surfaces thuscomputed in the global optimization routine module. The global objectivefunction has a gradient with respect to the camera internal and externalparameters that can be easily established thorough the chain rule: [Eq.(8)] $\begin{matrix}{\frac{\partial E}{\partial\left( {p_{i},\quad q_{i}} \right)} = {\sum\limits_{\quad j}^{\quad}\quad {\frac{\partial e_{ij}}{\partial M_{ij}}\frac{\partial M_{ij}}{\partial\left( {p_{i},\quad q_{i}} \right)}}}} & (8)\end{matrix}$

[0078] from using Eq. (2) and Eq. (7) above, as shown in FIG. 4 as box406. It has been found that since no direct evaluation on images isinvolved, the computation required using Eq. (7)-(8) as described abovein minimizing the global objective function for all the overlappingimages is nearly trivial. The computational savings using the techniquesdescribed herein result in several orders of magnitude in savings oftime and speed over prior techniques of optimization.

[0079] In the most general case, the camera parameters for each imageare four internal parameters, p_(i), and three orientation parametersqi. Every pairwise registration provides eight constraints on thosecamera parameters. When there are plenty of overlapping images pairs,the optimization is overconstrained, in that the number of independentparameters is generally less than that of the number of constraints.However, in practice, even when the optimization appears to beoverconstrained, oftentimes camera parameters are so weakly constrainedthat they can easily diverge the whole optimization.

[0080] In order to solve the aforementioned problem, so that theoptimization described herein behaves well in underconstrained or weaklyconstrained situations, it is preferred that simulated annealing be usedto dampen the camera internal parameters. Conceptually this step isshown in the generalized flowchart of FIG. 4 as box 408. As theoptimization progresses, the damping parameters are gradually reduced.The exposure parameters s_(ij) and b_(ij) are estimated through a linearregression. The proposed solution has been found to work remarkably wellin practice, and is a significant improvement over prior techniques.

[0081] The pairwise registration and global optimization described abovecan be iterated if the alignments are still not satisfactory, by eitherby a user acting through the user interface, or by automated means, asindicated by arrows 233 in FIG. 2 and boxes 418 and 420 in FIG. 4. Thus,in the iteration, the pairwise registration module 222 will use theimproved camera parameters generated by the calibration and globaloptimization module 224 to re-initialize the projective registrations,and re-compute the optimal projective matrices and their Hessians. Thenthe improved projective matrix parameters will, in turn, be used togenerate improved estimations of camera parameters in the globaloptimization module 224. Likewise, blending may be further iteratedafter registering, calibrating and optimizing the images after aninitial blending.

[0082] III. Blending

[0083] Notwithstanding the improved method and system of pairwiseregistration, camera calibration and global optimization of imagesdescribed above, it has been found that for high quality panoramasblending of overlapping image boundaries is often required prior toviewing the panorama. Such blending is required when the pairwiseregistration and global optimization by the system generates panoramashaving imperfectly aligned images that give “shadow” or “ghosting”effects, if the images are averaged in overlap regions. As human eyesare very sensitive to such imperfections, in one preferred embodimenthuman input may be used to facilitate proper blending during theauthoring of a panorama, using the system and method disclosed herein.Other methods for blending may also be employed in the presentinvention, such as the multi-resolution weighted average method, and theweighted average method. In the weighted average method, as illustratedin FIG. 9, there is a transition region 902 between images to beblended, Image 1 and Image 2. The weights of image 1 for intensity orother parameter is linearly decreased from a value of 1.0 to 0.0 in thetransition region, while the weights of Image 2 is increased from 0.0 to1.0. A pixel in the transition area is a weighted sum of two pixels fromtwo images.

[0084] By contrast, the multi-resolution weighted average method firstdecomposes two images into different frequency bands by buildingLaplacian pyramids, and performs separate weighted averages on eachpyramid level with different transition lengths for each frequency.Transition lengths are defined by the region it takes for a parameter togo from value 1 to 0 or 0 to 1. FIG. 8 shows the transition lengths fordifferent frequency bands (low, middle and high) of images, with highfrequency image components having a shorter transition length regionthan low frequency image components. The result of this multi-resolutionblending method is seamless and absent of shadow effects.Multi-resolution weighted average blending, known per se in the art, isfurther described in P. Burt and E. Adelson, “A multiresolution splinewith application to image mosaics”, ACM Transactions on Graphics,2(4):217-236 (1983). While multi-resolution blending described herein isthe preferred blending technique in a preferred embodiment-of theinvention, other types of blending, including simple weighted averageblending, is within the scope of the invention.

[0085] To determine the boundary of overlap regions to performmulti-resolution blending, preferably a blend mask is needed for anarbitrarily shaped transition region. The Gaussian pyramid of the maskimage supplies the weights for every pixel at every pyramid level. FIGS.10 (a) and (b) illustrate the blend mask 1000 used for the panoramiccanvas having two overlapping images, Image 1002 (Image 1) and 1004(Image 2). In order to maximize the size of the transition region forblending, the boundary curve of the mask inside the overlap regions,boundary 1001, needs. to be as far way as possible from the originalimage boundaries. To locate the mask boundary a grassfire transform ispreferably used on two images individually. The resulting distance mapsrepresent how far away each pixel is from its nearest boundary. Thepixel values of the blend mask is then set to either 0 or 1 by comparingthe distance values at each pixel in the two distance maps.

[0086] Generally, the grassfire transform measures distance by notingthe time it takes for a constant velocity wave front to reach a certainpoint, knowing that distance equals velocity multiplied by time.Conceptually, the distance is measured as if distance were measured bynoting the time elapsed that a grass fire, having constant velocity andlit on the edges of a grass field, progresses to the center of thefield. In this way the exact boundaries of the field do not have to besurveyed by more precise techniques of geometry. Further detailsregarding the grassfire transform, known per se in the art, can be foundin the literature, e.g., C. Arcelli, L. P. Cordella, and S. Levialdi, “Agrassfire transformation for binary digital pictures.”, ICPR74, pp.152-54 (1974). However, though the grassfire transform is preferred inone embodiment of the present invention, other techniques may be used togenerate a blend mask, such as solving directly a Laplacian differentialequation with predetermined boundary conditions to directly generate amask with the addition of a gray scale.

[0087] Regarding the blending procedure, the blending is achieved by thefollowing method. An empty panoramic canvas, which can simply be abuffer of memory in a computer system, such as memory 220 in FIG. 2, iscopied with the first image, Image 1. Second, new images are blendedonto the panoramic canvas one by one. For each of those new images, theblend mask from the panoramic canvas and the new image is generated.Next, there are computed Laplacian pyramids of the images and Gaussianpyramids of the masks in the bounded rectangular areas of the overlapregions. Multi-resolution blending is used to blend the Laplacian andGaussian pyramids. Finally, the blended images is copied onto thepanoramic canvas, which may hold other images.

[0088] The flowchart for this procedure, generally speaking, is alongthe lines as shown conceptually in FIG. 5, and as can be modified fromthe teachings of the present invention.

[0089] (1) determine the coarsest level resolution level of a Laplacianpyramid at which two images I_(i), I_(j), (or I, J) are to be blended(step 504). The bottom-most level is computed from computing theinertial tensor of the images I, J, which gives an inertial ellipsehaving a minor axis that is used to find the number of pyramid levels inthe Laplacian pyramid.

[0090] (2) From the overlapping images I, J construct a Laplacianpyramid (step 506), as is known per se in the art, starting at thefinest level of resolution and working through the pyramid to morecoarser levels of resolution.

[0091] (3) Generate a blend mask (step 508), preferably using thegrassfire transform described herein, and construct a Gaussian pyramidfrom the blend mask. The Gaussian pyramid may be constructed by applyinga low-pass filter to the blend mask, which dilutes the sharp edges, fromlinear interpolation between the black and white regions of the blendmask, or from other techniques.

[0092] (4) At each level in the Laplacian pyramid of images I, J thatare to be blended, blend the overlap regions, preferably by the methodof multiplying the Laplacian values of images I, J times the weightedvalues supplied by the Gaussian pyramid based blend mask, according tothe value for I times the mask value (MV), or the value for J times thecompliment of the mask value (1-MV), (step 510).

[0093] (5) Add the results at each level of the Laplacian pyramid (step512), until the finest level resolution of the Laplacian pyramid isreached (or upon user interruption, as always) (steps 512 and 514).

[0094] (6) Perform steps (1)-(5) for all images to be blended in theblend region (step 516). Previously blended images may be blended withnew images, and blending may be iterated, with human input orautomatically.

[0095] The net result of these steps is that the lowest frequencycomponent images are blended over the entire transition region, giving adesired smoother effect, while high frequency components (such as sharpedges) are blended over a smaller region, typically 3-5 pixels wide,which “sharpens” these high frequency components, as desired.Conceptually this is shown in FIG. 8, with the blending regions 802,804, 806 for the low, middle and high frequencies being shorter,respectively, according to the functioning of the blending module asdescribed.

[0096] The net visual effect of the blending described herein, besidesproducing a pleasing smoothing of images that helps eliminate ghosting,is an “auto-iris” effect, in that luminosity appears to be automaticallyadjusted when moving from a high intensity image to a low intensityimage, similar to the adjustments made by a human eye.

[0097] In practice, it has been found that on occasion, where there areoverlaps of more than two images, a-particular problem is encountered inthe blending of images, as illustrated graphically in FIG. 11(a). When afirst (N−1) images are sequentially blended onto the palnorama canvas,and there is an attempt to blend Image N, most of the area covered byImage N is already blended by an “unintended” overlap between Image 1and Image N−1, with the blend mask 1110 indicated generally as the grayarea inside the dotted lines. As a result, Image N has little effect onthe panorama even though it provides much large transition areas betweenImage 1 and Image N−1, and therefore has the potential to improve thequality of the panorama. In the most general case, because of the natureof panoramas, the problem illustrated by FIG. 11(a) has the potential tooccur on occasion.

[0098] One method to solve the problem illustrated by FIG. 11(a) duringauthoring of the panorama is to allow manual input to override thecomputer default ordering for the blending of images. Images with largeroverlaps (e.g., a very dark, low frequency image that may be abackground color to a series of high frequency lighter foregroundimages) should be blended onto the panoramic canvas first manually, andcan be selected for blending by a user of the present apparatus, througha suitable user interface that lists the images to be blended first in apriority list.

[0099] Another more automated method to solve the problem illustrated byFIG. 11(a) is illustrated conceptually in FIG. 11(b). The automatedsolution uses a labeling scheme. For every pixel on the panoramiccanvas, which may be a blended pixel, the computer labels it with anumber indicating which source image contributes the most to this pixel.In FIG. 11(b), the dashed line 1120 represents the blend mask boundarywhen Image 1 and Image N−1 are blended. The pixels on the left of thedashed line 1120 have label 1, as Image 1 contributes the most to thepixel values in that area of the panoramic canvas, while the pixels onthe right side of the dashed line 1120 have label N−1, as image N−1,which may be a previously blended image, contributes the most to thepixel values in that area. When another image, Image N. needs to beblended onto the panoramic canvas, first a grassfire transform on thepanoramic canvas is performed. In addition to the actual imageboundaries, the dashed line 1120, representing the blend mask boundarybetween images Image I and Image N−1, is regarded as a virtual boundary,or “firewall”, that the grassfire cannot penetrate. The virtualboundaries are computed easily using the pixel labels and the list ofall intended overlaps. The resulting blend mask is illustrated as thegray area 1130 in FIG. 11(b), which is much larger than the blend maskarea of FIG. 11(a). Using this “firewall” technique, the blending takesadvantage of both large overlaps between Image I and Image N, and ImageN and Image N−1, which alleviates the aforementioned problem associatedwith FIG. 11(a).

[0100] IV. HUMAN INTERFACE

[0101] Human interaction is an integral part of the method and apparatusof the present invention. The system of the present invention is tryingto solve a complicated nonlinear optimization problem. No automatedprocedure can guarantee its convergence to a global minimum; in thissense the system is heuristic. On occasion, human interaction-through auser interface can steer the system to produce a more satisfactorypanorama. Some areas of possible human interaction with the systeminclude manual projective registration, initial calibration, andfeedback generally.

[0102] In manual projective registration, human interaction is sometimesbeneficial in cases where the projective registration of images breaksdown due to factors such as excessive exposure difference, motion in thescene, bad initial estimates, and the like. When automatic registrationfails, human interaction through a user interface, such as through userinterface function module 230 of FIG. 2, allows for manual registration,through a windows-based interface, such as of the type discussed inconnection with FIG. 6. In this instance a human would manuallyinitially align images more precisely (relying on eyesight and a mousepointer, or, by manually entering via a keyboard the coordinates forpositioning an image) for either pairwise local registration or globalregistration, in order to then allow the computer to automaticallyoptimize the images as discussed herein. The user would not supersedethe system of the present invention, but assist the system to allow forthe automatic convergence to a solution.

[0103] Similarly, in. initial calibration, e.g., step 314 in theembodiment of FIG. 3, the number of camera internal and externalparameters is large in the general case. The global optimizationfunction module needs initial conditions in order to converge to theright answer. A user interface, such as of the kind discussed in FIG. 6,provides an interactive tool to initialize those parameters. Thus, inthe event the user has more accurate information about initialparameters than is supplied by the computer default parameters, the usercan input those parameters.

[0104] Human interaction; is present throughout to provide feedback tothe computer system of the present invention. The system must have theability to provide feedback in all the nonlinear optimizations to letusers monitor the progress of the system, and allow them to intervenewhen necessary. In a preferred embodiment, the user interface for humaninteraction may be a real-time texture map engine which simulates avirtual camera looking out from the common nodal point of therectilinear images. All images are seen floating in 3D space. The usercan select any image and change its internal and external parametersinteractively in real time. In one preferred embodiment, the images maybe seen as if the user was situated inside of a sphere, termed aspherical coffee-table, illustrated conceptually as virtual realityspace in FIG. 12, with the images 1210 presented tangent to the outsideof the viewing sphere 1220. The-arrangement of the images outside thesphere may be arranged by a virtual reality type authoring userinterface, with the use free arrange which images will be blended, andwhere, by placing the wing sphere 1220. Details of this interface can beimplemented by one of ordinary skill in the art using the teachings ofthe present invention. The images, once selected by a user, are pairwiseregistered, calibrated, globally optimized and blended, as taughtherein, to construct a panorama that may then be projected onto asphere, producing a 3D panorama viewing space.

[0105] Although the present invention has been described in terms of thepreferred embodiments above, numerous modifications and/or additions tothe above-described preferred embodiments would be readily apparent toone skilled in the art. It is intended that the scope of the presentinvention extends to such modification and/or additions and that thescope of the present invention is limited solely by the claims set forthbelow.

We claim:
 1. A computer system for authoring panoramas, comprising:memory storing data representations of a plurality of images; I/O forinputting and outputting data; function modules in said memory; aprocessor cooperating with said memory and I/O for processinginstructions and data from said memory, said I/O and said functionmodules; a pairwise registration function module in said memory andoperating said processor for pairwise registration of said images, saidpairwise registration function module generating output data related tosaid pairwise registration of said images; a calibration and globaloptimization function module in said memory and operating said processorfor calibration and global optimization of said output data of saidpairwise registration module, said calibration and global optimizationmodule generating output data related to said calibration and globaloptimization of said images; a blending function module in said memoryand operating said processor for generating at least one panorama fromsaid output data from said pairwise registration module and saidcalibration and global optimization module; and a projection functionmodule in said memory and operating said processor for forming apanorama from said images.